1. Field of the Invention
The present invention relates to a method for controlling a rolling process in a hot strip finish rolling mill. More particularly, this invention relates to a method and an apparatus for controlling a rolling process in a hot strip finish rolling mill to make the sheet profile of a strip at the outlet side of the final stand precisely coincide with a desired sheet profile.
2. Description the Related Art
In a hot strip finish rolling mill, the sheet thickness, the distribution of the sheet thickness (the sheet profile) across the width of the strip and the flatness and the like of the sheet are controlled. The sheet profile or the sheet crown is controlled by controlling crown control devices, disposed at each rolling stand forming the finish rolling mill. The crown control devices are controlled to make the sheet profile at the outlet side of the final rolling stand coincide with a desired sheet profile.
Therefore, in a conventional rolling mill, a sheet profile meter for measuring the sheet profile is disposed at the outlet side of the final rolling stand of the finish rolling mill. The results from the sheet profile meter are used to control the sheet profile of the product rolled by the final rolling stand. Further, a model for controlling the sheet profile is modified to minimize the control error for the next material to be rolled.
In this conventional sheet profile control system, a control model equation, shown in Equation (1), is used. In a tandem rolling mill having N stands, an equation corresponding to Equation (1) is used for each stand. This creates a system of N simultaneous equations. The desired sheet profile at the outlet side of the final rolling stand is obtained by solving for this system of equations. Equation (1) states: EQU Cr.sub.i =.alpha..sub.i .multidot.Crm.sub.i +.beta..sub.i .multidot.Cr.sub.i-1 ( 1)
where Cr.sub.i is the sheet profile on the outlet side of the i.sup.th rolling stand, counted from the upstream to the downstream stand, Crm.sub.i is a so-called mechanical crown of the i.sup.th rolling stand, Cr.sub.i-1 is the sheet profile of the outlet side of the i-1.sup.th, or immediately upstream stand, .alpha..sub.i is the imprinting ratio of the mechanical crown of the i.sup.th rolling stand and .beta..sub.i is crown heredity coefficient of the sheet profile of the immediately upstream rolling stand. These factors will now be described.
The mechanical crown Crm.sub.i in Equation (1) is the amount of mechanical crown occurring due to deflection of the roll caused by the rolling load, by the thermal expansion of the roll or from the wear of the roll. Defining the crown occurring due to the deflection of the roll caused from the rolling load as Cmp.sub.i, the crown occurring due to the thermal expansion of the roll as CmRh.sub.i, and the crown occurring from the wear of the roll as CmRw.sub.i, the foregoing mechanical crown Crm.sub.i is expressed by equation (2): EQU Crm.sub.i =Cmp.sub.i +CmRh.sub.i +CmRw.sub.i ( 2)
The crown Cmp.sub.i in Equation (2), occurring due to the deflection of the roll is, in accordance with the widthwise directional load distribution, given from: 1) the deflection of the work roll and the backup roll (in addition, any change occurring due to the output from the crown control apparatus is included in the Cmp.sub.i factor); and 2) the function f.sub.1 expressed in Equation (3). Equation (3) is formulated by considering the initial crown of the roll. In the following equation, P is the rolling load, b is the width of the material and x is the output from the crown control apparatus. EQU Cmp.sub.i =f.sub.1 (P, b, x) (3)
The heat crown CmRh.sub.i occurring due to the thermal expansion of the roll is determined from the change in the roll crown as the sheet is rolled and cooled after rolling. Specifically, the heat crown is determined by, for example, first-order response lag approximation and by obtaining each time constant and proportional constant and the like from experimental data by means of regression.
If the surface condition of the roll changes when the heat crown is determined, such that a black skin forms or separation takes place as the sheet is rolled in the hot strip finish rolling mill and such that the resulting change in the frictional coefficient or the heat transference coefficient changes the amount of heat flowing from the strip to the roll, an estimation error in the heat crown occurs. However, such a change in the heat flow cannot be measured. Thus, the error in the estimated heat crown cannot be precisely determined.
The wear crown CmRw.sub.i occurring due to the wear of the roll is expressed by Equation (4), defining the function f.sub.2, where C.sub.f is a friction coefficient, L is length of rolling and D is the diameter of the roll. EQU CmRw.sub.i =C.sub.f .multidot.f.sub.2 (P, L, b, D) (4)
In Equation (4), C.sub.f is determined from regression of the result of rolling the sheet. However, the degree of the wear of the roll changes due to the characteristics of the sheet's material and the surface condition of the sheet. Therefore, errors occur when estimating the wear crown CmRw.sub.i due to the wear of the roll.
The imprinting ratio .alpha..sub.i in Equation (1) is given by function f.sub.3 expressed by Equation (5): EQU .alpha..sub.i =f.sub.3 (h, L.sub.d, K.sub.ch, .xi.) (5)
where h is the sheet thickness on the outlet side of the i.sup.th rolling stand), L.sub.d is the length of the contact arc, K.sub.ch is the regression coefficient, which changes with the sheet width, the length of the contact arc and the deformation resistance and the like, and .xi. is a shape factor given by function f.sub.4 expressed by Equation (6): EQU .xi.=f.sub.4 (D, h, b) (6)
The crown heredity coefficient .beta..sub.i is given by function f.sub.5 expressed by Equation (7), where H is the sheet thickness on the inlet side (of the i.sup.th rolling stand): EQU .beta..sub.i =f.sub.5 (K.sub.ch, L.sub.d, .xi., h, H) (7)
The imprinting ratio .alpha..sub.i in Equation (5) and the crown heredity coefficient .beta..sub.i in Equation (7) have, as variables, the regression factor K.sub.ch and the shape factor .xi. which can be obtained from regression. However, the variables .alpha..sub.i and .beta..sub.i are determined experimentally.
A conventional and usual sheet profile control method using Equation (1) will now be described, relating to a hot strip finish rolling mill having seven stands (first to seventh stands F1 to F7).
First, the strip pass schedule for the finish rolling is estimated. The rolling load to be applied at each stand is calculated to obtain the desired final percentage sheet crown Rc.sub.7.sup.Des (=Cr.sub.7.sup.Des h.sub.7) from the sheet thickness on the outlet side of the finish rolling mill. The percentage sheet crown Rc.sub.7.sup.Des is the ratio of the sheet thickness h.sub.7 on the outlet side of the seventh stand F7 and the desired sheet crown Cr.sub.7.sup.Des of the seventh stand F7. Further, the percentage sheet crown is used to determine the desired crown Cr.sub.i.sup.Des =Rc.sub.7.sup.Des .multidot.h.sub.i on the outlet side of each stand F1-F7 in accordance with the pass schedule.
Then, the desired mechanical crown Crm.sub.1.sup.Des for achieving the desired sheet crown Cr.sub.i.sup.Des for each stand is determined from Equation (1). Further, the output from the crown control apparatus necessary to achieve the desired mechanical crown is determined.
Then, the strip is actually rolled. The sheet crown Cr.sub.7 at the final stand F7 is measured by the sheet profile meter disposed at the outlet side of the final stand F7. The measured crown Cr.sub.7 at the outlet side is used to obtain the actual percentage sheet crown Rc.sub.7 (=Cr.sub.7 /h.sub.7).
Then, the percentage sheet crown at the outlet side of each stand is assumed to be the same as the actual percentage sheet crown Rc.sub.7 at the outlet side of the seventh stand F7. The actual rolling load at each stand and the actual percentage sheet crown Rc.sub.7 are used to obtain the error S.sub.i at each stand from Equation (1). That is, the sheet crown Cr.sub.i on the outlet side of the i.sup.th stand is obtained from Rc.sub.7 .times.h.sub.i, and the error S.sub.i that makes Equation (8) true is obtained. It should be noted that the mechanical crown Crm.sub.i is calculated by using the actual rolling load. Equation (8) states: EQU Cr.sub.i =.alpha..sub.i .multidot.Crm.sub.i +.beta..sub.i .multidot.Cr.sub.i-1 +S.sub.i ( 8)
After the sheet crown Cr.sub.i for each stand has been calculated from Equation (8), the control model is modified using Equation (8) to set the crown for the next material to be rolled. In addition, the error S.sub.i is used to obtain an adequate value for the mechanical crown Crm.sub.i so that the sheet crown at the outlet side of each stand will coincide with the desired sheet crown. Feedback control is also used so that the output from the crown control apparatus of each stand is changed to coincide with the obtained mechanical crown Crm.sub.i.
As specifically described above, the conventional hot strip finish rolling mill employs a method for controlling the sheet profile control apparatus for each stand based on the results of the measurement performed by the sheet profile meter disposed at the outlet side of the final stand.
The substantially same conventional rolling mill is disclosed in, for example, Japanese Patent Laid-Open No. 60-223605, which discloses using one sheet profile control apparatus for the final stand of the finishing mill, and one sheet profile control apparatus for a stand disposed upstream one stand from the final stand, to control the sheet profile and the sheet shape. Thus, the sheet crown and the sheet shape are controlled to desired values so that both the desired sheet crown and the desired sheet shape are obtained in the milling process. However, this method risks that the shape will be distorted between the final stand and the stand upstream one stand from the final stand, which causes the rolling operation to encounter a problem.
In order to prevent distortion of the sheet at the intermediate stand, methods for controlling through the upstream stand are disclosed in Japanese Patent Laid-Open No. 60-127013, Japanese Patent Laid-Open No. 63-199009 and Japanese Patent Laid-Open No. 1-266909. Generally, control performed prior to the intermediate stage of the finishing mill is effective for the hot rolling operation because the strip is thin and the crown control ability is unsatisfactory at the last stands. Therefore, the methods disclosed in these references are effective control methods because the control is performed prior to the last stand(s)..
Further, Japanese Patent Laid-Open No. 62-168608 and Japanese Patent. Laid-Open No. 2-37908 each discloses a control method in which a sheet profile meter is disposed on the inlet side of a tandem rolling mill.
Japanese Patent Laid-Open No. 59-39410 discloses measuring the sheet profile at the forward stand to control the sheet profile at the forward stand based on the measurement, coarsely controlling the shape at the rear stand, measuring the flatness on the outlet side of the final stand, and precisely controlling the flatness at the rear stand based on the measurement.
However, the methods disclosed in Japanese Patent Laid-Open No. 60-127013 and the like require a too long conveyance time between adjacent stands. Therefore, the control system wastes time. As a result, unsatisfactory control response occurs in these systems.
The method disclosed in Japanese Patent Laid-Open No. 62-168608 encounters a problem in that no significant effect on the sheet profile can be obtained in the hot rolling process because the metal flow is too large in the widthwise direction of the strip. Therefore, the influence on the change in the sheet profile on the inlet side of the tandem rolling mill is limited.
The method disclosed in Japanese Patent Laid-Open No. 59-39410 performs feedback control using the sheet profile measured at the forward stand. However, the percentage sheet crown can change without any distortion in the shape in the rear of the intermediate stand, because the strip is thick in the hot rolling process. As a result, an excessive error occurs in the intermediate stand even if feedback control is performed. Accordingly, control of the sheet profile on the outlet side of the final stand is unsatisfactory. Moreover, the obtainable effect is unsatisfactory in a case where the shape is feed-forward-controlled.